Rewrite The Following Equation In Slope-intercept Form: 5 X + 8 Y + 19 = 0 5x + 8y + 19 = 0 5 X + 8 Y + 19 = 0 Write Your Answer Using Integers, Proper Fractions, And Improper Fractions In Simplest Form.
Introduction
In mathematics, the slope-intercept form of a linear equation is a fundamental concept that helps us understand the relationship between the variables in an equation. The slope-intercept form is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. In this article, we will rewrite the given equation in slope-intercept form and provide the solution using integers, proper fractions, and improper fractions in simplest form.
The Given Equation
The given equation is . To rewrite this equation in slope-intercept form, we need to isolate the variable y.
Step 1: Subtract 5x from both sides
Subtracting 5x from both sides of the equation, we get:
Step 2: Subtract 19 from both sides
Subtracting 19 from both sides of the equation, we get:
Step 3: Divide both sides by 8
Dividing both sides of the equation by 8, we get:
Simplifying the Equation
The equation can be simplified by combining the fractions:
Conclusion
In this article, we have rewritten the given equation in slope-intercept form. The final equation is . This equation represents a linear relationship between the variables x and y, where the slope is -5/8 and the y-intercept is -19/8.
Understanding the Slope-Intercept Form
The slope-intercept form of a linear equation is a powerful tool for understanding the relationship between the variables in an equation. By rewriting the equation in slope-intercept form, we can easily identify the slope and the y-intercept, which can be used to graph the line and solve for the variables.
Graphing the Line
To graph the line, we can use the slope-intercept form of the equation. The slope is -5/8, which means that the line will have a negative slope. The y-intercept is -19/8, which means that the line will intersect the y-axis at the point (0, -19/8).
Solving for the Variables
To solve for the variables, we can use the slope-intercept form of the equation. We can substitute the values of x and y into the equation and solve for the other variable.
Example
Suppose we want to find the value of y when x = 4. We can substitute x = 4 into the equation and solve for y:
Therefore, the value of y when x = 4 is -39/8.
Conclusion
Q: What is the slope-intercept form of a linear equation?
A: The slope-intercept form of a linear equation is a mathematical expression that represents a linear relationship between two variables, x and y. It is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
Q: How do I rewrite an equation in slope-intercept form?
A: To rewrite an equation in slope-intercept form, you need to isolate the variable y. This can be done by subtracting the x-term from both sides of the equation, then dividing both sides by the coefficient of y.
Q: What is the slope of a line in slope-intercept form?
A: The slope of a line in slope-intercept form is the coefficient of the x-term, which is the number that multiplies the x-variable. In the equation y = mx + b, the slope is m.
Q: What is the y-intercept of a line in slope-intercept form?
A: The y-intercept of a line in slope-intercept form is the constant term, which is the number that is added to the product of the slope and the x-variable. In the equation y = mx + b, the y-intercept is b.
Q: How do I graph a line in slope-intercept form?
A: To graph a line in slope-intercept form, you can use the slope and the y-intercept to find two points on the line. The slope tells you the direction of the line, and the y-intercept tells you where the line intersects the y-axis.
Q: Can I use the slope-intercept form to solve for the variables?
A: Yes, you can use the slope-intercept form to solve for the variables. By substituting the values of x and y into the equation, you can solve for the other variable.
Q: What are some common mistakes to avoid when rewriting an equation in slope-intercept form?
A: Some common mistakes to avoid when rewriting an equation in slope-intercept form include:
- Not isolating the variable y
- Not dividing both sides of the equation by the coefficient of y
- Not simplifying the equation
- Not checking the equation for errors
Q: Can I use the slope-intercept form to find the equation of a line that passes through two points?
A: Yes, you can use the slope-intercept form to find the equation of a line that passes through two points. By finding the slope and the y-intercept, you can write the equation of the line in slope-intercept form.
Q: How do I find the slope and the y-intercept of a line that passes through two points?
A: To find the slope and the y-intercept of a line that passes through two points, you can use the following steps:
- Find the slope by using the formula m = (y2 - y1) / (x2 - x1)
- Find the y-intercept by using the formula b = y1 - m(x1)
Q: Can I use the slope-intercept form to find the equation of a line that is parallel to another line?
A: Yes, you can use the slope-intercept form to find the equation of a line that is parallel to another line. By finding the slope of the original line, you can write the equation of the parallel line in slope-intercept form.
Q: How do I find the equation of a line that is parallel to another line?
A: To find the equation of a line that is parallel to another line, you can use the following steps:
- Find the slope of the original line
- Write the equation of the original line in slope-intercept form
- Use the slope-intercept form to write the equation of the parallel line
Conclusion
In this article, we have answered some frequently asked questions about the slope-intercept form of a linear equation. We have discussed how to rewrite an equation in slope-intercept form, how to graph a line in slope-intercept form, and how to solve for the variables. We have also discussed some common mistakes to avoid and how to find the equation of a line that passes through two points or is parallel to another line.